Map Wars

Map wars
The Peters projection map of the world is one of the most controversial ever
produced. Peter Stalker explains why some professional map-makers hate it.

This is an odd edition of the NI. Or at least odder than usual. It unfolds into a colourful series of maps - from the new Peters Atlas - showing the global distribution of everything from cattle and cotton to calories and Christianity.

Readers with long memories will recall a similar surprise back in April 1985 when the magazine took the form of a fold-out world map. This was the Peters projection and NI readers had in their hands the original English edition of this remarkable new view of the world. Since then our translation of the map has appeared in many other shapes, sizes and imprints. Over three million copies have been distributed in the UK alone. You almost certainly have one yourself since new subscribers often receive a world map as a free gift.

The Peters projection has always been controversial. It looks strange and distorted - like passing the globe through a hall of mirrors and taking a snapshot of the reflection. Many people find it disturbing. And some academic cartographers are provoked into fits of rage by the very mention of the Peters projection, accusing it of all sons of sins. But one cannot really say that the Peters projection is 'wrong' or distorted. Nor can one say it is 'right' or 'true'; it is only another way of looking at things.

Any map of the world expresses a point of view. A correct model of the earth is a sphere - or an ellipsoid if you wish to be precise. Photographs of the earth from space provided comforting reassurance on that point. And if you wish to sense the relative positions of continents and oceans you should go out and buy yourself a globe and twirl it around.

But a globe cannot be pinned to a wall or printed in a magazine. For that you need a two-dimensional representation. This is where the problems start since you cannot project three-dimensional information onto a flat plane without making certain assumptions. The arguments between cartographers mostly concern what those assumptions should be.

One of the longest-lived projections was based on the needs of sixteenth-century navigators. Gerhard Kremer, a Flemish mathematician, produced his view of the world in 1569. Kremer translates to merchant in English and Mercator in Latin. And the Mercator projection survives to this day in many a book and map. It is a form of 'cylindrical' projection - what you get by wrapping a sheet of paper round a globe and simply transferring the information across (Figs. 1 and 2). This means that it indicates true North and South. So Newfoundland is directly north of Venezuela and it appears that way on the map. East and West similarly are also indicated correctly. Such a map demonstrates what is called 'fidelity of axis'.

Mercator's version of this (Fig. 30 also shows intermediate compass directions like North-west more or less accurately. So it is possible to conclude from his map that Brazil is South-west of Liberia and if you plot course in that direction you will eventually arrive at your destination. No wonder it was appreciated by the early explorers. If it can be used in this way a map is said to have 'fidelity of angle'.

But fidelity of angle is only achieved at a cost. To make it work, the further away you get from the Equator the further apart you have to move the horizontal lines of latitude. As these distances increase so do the sizes of the countries underneath them. So by the time you get to the North or South Poles the lines would be drawn infinitely far apart and the Arctic and Antarctic regions can scarcely be represented at all since they would be infinitely large. More importantly the relative sizes of intermediate areas are completely distorted; South America seems smaller than Europe whereas in fact it is twice the size. These changes in scale also distort the shape of countries.

Given such defects it's surprising that the Mercator projection has survived so long especially as dozens of other more satisfactory projections have appeared since. These have usually attempted to represent country sizes and shapes more correctly. But to do so they have had to make a compromise - they have 'bent' the lines of latitude and longitude. Fidelity of axis has thus been lost and you can no longer judge North, South, East and West so easily. There have been dozens of projections to choose between, from Van der Grinton through Aitoff (Fig. 4) to Robinson. Most of us, however, did not bother to distinguish between them or even notice that they were different from Mercator. We assumed that all maps were simply factual statements.

Then along came Dr Arno Peters, a German historian. He was irritated by the maps he saw widely published and was particularly incensed by the survival of Mercator. This, he argued, gave a Euro-centric view of the world: it shrank the developing countries since most of these are around the Equator; and it expanded the richer countries since they lay further north. Even the Equator itself is shown two thirds of the way down the traditional Mercator map. None of this was Mercator's fault of course - his map was designed for a specific job which it did pretty well.

FIGURE 1
Wrapping a sheet of paper round a globe and transferring the information across to it horizontally gives a 'cylindrical' projection.

FIGURE 2
This map will portray countries at the Equator fairly accurately but seriously distorts those nearer the poles. Lines of latitude are squeezed closer and closer together. North, South, East and West directions are 'true' on this map. But intermediate bearings like North-west cannot be plotted as straight lines.

FIGURE 3
Mercator's projection moves the places on the map so that they fall under correct compass bearings. But to achieve this the lines of latitude have to be moved further apart as you near the poles.

FIGURE 4
Subsequent attempts, like Aitoff's, to indicate relative country size more accurately usually use 'rounded' grids and so lose fidelity of axis. To see if a point lies south, say, of any other you must follow the grid lines. On simpler maps these are often left out.

Dr Peters did not have to devise a map of his own to improve upon Mercator. He could have seized upon any one of the subsequent proposals and promoted its use. But none entirely satisfied him. He insisted first that a map for general use should be an equal-area projection so that no country is given prominence over another. He also insisted on fidelity of axis to avoid the disorientating effect of bent lines of latitude and longitude.

Then there is the question of country shape. If you were to take a photo of a globe in its normal position you would find the countries round the Equator like Zaire or Ecuador came out of it pretty well. They would be shown relatively large and with something close to their correct shape. But further north or south there are considerable distortions: Australia tails away alarmingly. One of Dr Peters' most significant and controversial decisions was that the minimum distortion should occur not at the Equator but at the 45-degree lines of latitude. His argument was that these were much more populated areas. Fair enough, except that this works counter to his intention to treat the Third World more justly, for it significantly changes the shape of both Africa and South America.

Given his criteria, the Peters map more or less draws itself: that's the way it has to be. It has the added advantage that this series of choices also produces a shape close to the 'golden section" said to be pleasing to the human eye.

Not all eyes however. The projection has been remarkably controversial, partly because the Peters map does radically change some country shapes. All projections distort to some extent. But it is clear that Africa appears exceptionally long and thin on the Peters map.

But the oddity of the Peters projection is at least partly responsible for its success. It draws attention to its claims and particularly that of equality of area. For almost the first time there has been widespread discussion on the misrepresentation of country sizes in previous maps. Third World countries and those organizations interested in promoting international development have seized on it as a means of provoking debate. Indeed it is now almost de rigueur for the Peters map to be used if your intention is to express solidarity with the Third World.

Dr Peters' character has also been important to the map's success. He has been a tireless promoter and very effective publicist of his ideas. Even the best ideas need selling and Dr Peters has sold this one very well - much to the chagrin of the previously staid world of map-drawing.

'The Peters phenomenon has plagued the world of professional cartographers,' complains UK writer John Loxton He raises some technical question about calculation methods but the gist of the criticism is that Peters has been too successful - effectively excluding other projections from consideration. A statement by the German Cartographical Society, 'The So Called Peters Projection', similarly rails against Peters for claiming originality when projections similar to his (specifically that of Gall) have appeared earlier without much success. It must be particularly galling for these professional map-makers that the initiative has been seized not by a cartographer or geographer but by an historian.

'The real danger,' writes US cartographer Arthur Robinson, 'is not the projection (Peters) is pushing but instead the long-term harm that can be done to the profession as a consequence of the techniques Peters is using to promote his map. He is clever.' Mr Robinson. it should be added, is the author of the projection recently issued by National Geographic. He describes the land masses shown on the Peters projection as 'somewhat reminiscent of wet, ragged, winter underwear hung out to dry on the Arctic circle'.

The issues which the Peters map raises are relatively simple. If you decide you want an equal-area map with fidelity of axis you will always get something resembling the Peters projection. If you decide that shape is more significant than fidelity of axis you will get something else.

The real value of the Peters projection is that it has made the world think about something that before was never taken seriously: that maps of the world represent a point of view just as do press articles or TV programmes or photographs. We wouldn't recommend you navigate a 747 round the world with the Peters projection - or with any other single global projection if it comes to that for they would all lead you astray. But if you want to stir things up then the Peters projection is a real winner.

NI readers get another opportunity this month with the publication of the Peters Atlas of the World. We are grateful to Dr Peters and to Longman, his publishers, for the opportunity to offer an advance preview of some of its thematic maps.

1 For a rectangle this shape is the one where the smaller side is to the larger as the larger is to the sum of the two.2The Cartographic Journal, Vol.22 December 1985.3 A translation appears in the above journal.4The American Cartographer, Vol. 12, No. 2, 1985.

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